Quickest Flows Over Time

Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Traditionally, flows over time are solved in time‐expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time‐expanded network. We present several approaches for coping with this difficulty. First, inspired by the work of Ford and Fulkerson on maximal s‐t‐flows over time (or “maximal dynamic s‐t‐flows”), we show that static length‐bounded flows lead to provably good multicommodity flows over time. Second, we investigate “condensed” time‐expanded networks which rely on a rougher discretization of time. We prove that a solution of arbitrary precision can be computed in polynomial time through an appropriate discretization leading to a condensed time‐expanded network of polynomial size. In particular, our approach yields fully polynomial‐time approximation schemes for the NP‐hard quickest min‐cost and multicommodity flow problems. For single commodity problems, we show that storage of flow at intermediate nodes is unnecessary, and our approximation schemes do not use any

Maximum Contraflow Evacuation Planning Problems On Multi-network

Contraflow approach for the evacuation planning problem increases outbound capacity of the evacuation routes by the reversal of anti-parallel arcs, if such arcs exist. The existing literature focuses on network contraflow problems that allow only anti-parallel arcs with equal transit time. However, the problems modeled on multi-network, allowing parallel as well as anti-parallel arcs with not necessarily equal transit time, seem more realistic. In this paper, we study the maximum dynamic contraflow problem for multi-network and propose efficient solution techniques to them with discrete as well as continuous time settings. We also extend the results to solve earliest version of the problem for two terminal series parallel (TTSP) multi-network

An annotated overview of dynamic network flows

The need for more realistic network models led to the development of the dynamic network flow theory. In dynamic flow models it takes time for the flow to pass an arc, the flow can be delayed at nodes, and the network parameters, e.g., the arc capacities, can change in time. Surprisingly perhaps, despite being closer to reality, dynamic flow models have been overshadowed by the classical, static model. This is largely due to the fact that while very efficient solution methods exist for static flow problems, dynamic flow problems have proved to be more difficult to solve. Our purpose with this overview is to compensate for this eclipse and introduce dynamic flows to the interested reader. To this end, we present the main flow problems that can appear in a dynamic network, and review the literature for existing results about them. Our approach is solution oriented, as opposed to dealing with modelling issues. We intend to provide a survey that can be a first step for readers wondering whether a given dynamic network flow problem has been solved or not. Besides restating the problems, we also describe the main proposed solution methods. An additional feature of this paper is an annotated list of the most important references about the subject

DOWNSTREAM RESOURCE ALLOCATION IN DOCSIS 3.0 CHANNEL BONDED NETWORKS

Modern broadband internet access cable systems follow the Data Over Cable System Interface Specification (DOCSIS) for data transfer between the individual cable modem (CM) and the Internet. The newest version of DOCSIS, version 3.0, provides an abstraction referred to as bonding groups to help manage bandwidth and to increase bandwidth to each user beyond that available within a single 6MHz. television channel. Channel bonding allows more than one channel to be used by a CM to provide a virtual channel of much greater bandwidth. This combining of channels into bonding groups, especially when channels overlap between more than one bonding group, complicates the resource allocation problem within these networks. The goal of resource allocation in this research is twofold, to provide for fairness among users while at the same time making maximum possible utilization of the available system bandwidth. The problem of resource allocation in computer networks has been widely studied by the academic community. Past work has studied resource allocation in many network types, however application in a DOCSIS channel bonded network has not been explored. This research begins by first developing a definition of fairness in a channel bonded system. After providing a theoretical definition of fairness we implement simulations of different scheduling disciplines and evaluate their performance against this theoretical ideal. The complexity caused by overlapped channels requires even the simplest scheduling algorithms to be modified to work correctly. We then develop an algorithm to maximize the use of the available system bandwidth. The approach involves using competitive analysis techniques and an online algorithm to dynamically reassign flows among the available channels. Bandwidth usage and demand requests are monitored for bandwidth that is underutilized, and demand that is unsatisfied, and real time changes are made to the flow-to-channel mappings to improve the utilization of the total available bandwidth. The contribution of this research is to provide a working definition of fairness in a channel bonded environment, the implementation of several scheduling disciplines and evaluation of their adherence to that definition, and development of an algorithm to improve overall bandwidth utilization of the system

On Evacuation Planning Optimization Problems from Transit-based Perspective

Increasing number of complex traffic networks and disasters today has brought difficulty in managing the rush hours traffic as well as the large events in urban areas. The optimal use of the vehicles and their assignments to the appropriate shelters from the disastrous zones are highly complicated in emergency situations. The maximum efficiency and effectiveness of the evacuation planning can be achieved by the appropriate and significant assignment of the transit dependent vehicles during pre and post-disaster operations. This paper presents a comprehensive overview of the evacuation planning optimization techniques developed over the years, emphasizing the importance of their formulation and the solution strategies on disaster management from the transit-based perspective. Each technique is briefly described and presented lucidly with some of its known applications, significances, and solution strategies expecting that it should be able to guide much more interest into this important and growing area of research

Earliest Arrival Flows with Multiple Sources

Earliest arrival flows capture the essence of evacuation planning. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink "as quickly as possible". The latter requirement is made more precise by the earliest arrival property which requires that the total amount of flow that has arrived at the sink is maximal for all points in time simultaneously. It is a classical result from the 1970s that, for the special case of a single source node, earliest arrival flows do exist and can be computed by essentially applying the Successive Shortest Path Algorithm for min-cost flow computations. While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open for many years. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem